Understanding Electrical Potential and potential difference.

[christian0710]

Hi, I'm trying to understand electrical potential and potential difference. I was wondering if anyone can confirm if what I have written is correct or not? If not I would be glad to learn what I am yet not understanding.

When you push away an electron of negative charge from a positive charge, you increase its potential energy because it requires work to push it against its will. The work done on the electron when pushing it towards the negative charge is stored in the electron as potential energy. The reason electrons have high potential energy when leaving the negative pole of a battery, is because they are forced close to a negative pole.
The potential difference in a battery depends on the difference in charge between the positive and negative pole in the battery, and the bigger the potential difference the faster the electrons run through the system, and the more energy they drop off in form of heat or light.

 

[mfb]

against its will

The electron does not have its own will. You push it against the attractive force.

The potential difference in a battery depends on the difference in charge between the positive and negative pole in the battery

Usually, batteries do not have "a big positive charge" at one pole and "a big negative charge" at the other one. They store the energy in a chemical way. Capacitors can have that charge separation, but they have a lower capacity.

and the bigger the potential difference the faster the electrons run through the system

No. And the speed of electrons is quite unintuitive and not useful when you analyze circuits.*
You probably mean the current flow, but that depends on the potential difference and the resistance of the circuit.

and the more energy they drop off in form of heat or light.

Or other types of energy.*you can calculate the average, effective (!) speed of electrons in cables, and get results of millimeters per second

 

[sophiecentaur]

There is a temptation to confuse the energy situation of a charged particle when it is out in space or in the low density situation in a gas and when it is in the confines of a dense (solid or liquid) conductor. It is easy to talk in terms of the fields between two parallel plates and the resulting force on an electron between them. The force is just Volts per Metre times the charge and the work done in moving it around is just the force times the distance moved.
When you have zillions of electrons in a circuit, in the presence of an equal number of zillions of protons and you connect a battery, how do you define the fields involved? The wires could be a few cm or tens of metres long so the simple 'volts per metre' is not a useful quantity. That's why electrical calculations just use Potential, which tells you how much Energy is involved in shifting a given Charge - Volts per Coulomb. This quantity has far more meaning (mostly) when you are doing 'circuits'. 'PD' rules for circuits.
Many people try to talk about electrons when trying to 'understand' electronics and this must be down to the way 'they' teach it in School. It's much better to think 'Current, Charge and Volts' like the rest of electronics and electrical Engineers. This isn't a cop out, it's just the most fruitful approach - in the same way as mechanical Engineers design and test bridges etc. using the bulk qualities of the materials that they use.
Of course there is a relationship between the two levels of approach but you only need to consider it on rare occasions.

 

[christian0710]

Hey guys, thank you for your help I appreciate it. I have now rewritten the definition of potential energy, electric potential energy and potential difference.
I would really appreciate if someone could tell me if this definition is correctly understood :)

At the bottom I have a question regarding the difference between electric force and electric potential energy

Definition and how it all works

Electrical potential Energy (or Electrostatic potential energy)
Symbol U_E
SI unit = Joule
If we have some charge q_s (fx electrons) at some point in space, they create electric fields (with the symbol E). The electrical field created by the charge, can exert an electric force on another charge q_t (electric force is like an invisible spring repelling or pulling one charge towards another). If you push the charge q_t closer to q_s the electric field created by q_s will exert force upon q_s (attract or repel it) The work done on q_t in order to move it toward the charge q_s (given q_t and q_s have opposite signs so they repel each other) will be stored in q_t as electric potential energy.

The electric field (created by a charge) at a point in space tells us how much force (in Newton) one coulomb of a test charge would feel in that field. The force exerted onto the charge by the electric field is called electric force and has the unit Newton.
F_{(electric force)}=q_t*E=coulumb*Newtons/Coulumb=Newtons
This shows the force a test charge would feel in an electric field created by other charges.

Electric field vs. Electric potential (voltage)

Electric field E=Newtons/Coulumb
This shows that one charge put in an electric field would feel X amount of Newtons excerted onto it by the electrc field.

Electric potential V=Joules/Coulumb=(Electric potential energy)/Coulumb=Volt
This shows the amount of electric potential energy one coulomb of charge would feel at a point in space. Electric potential Energy # Electric potential. Electric potential energy U=Joules
The Electric potential difference is the difference in electric potential (∆Volt). When moving the charge from A to B (IN AN ELECTRIC FIELD I ASSUME?) there will be a drop or increase in its electric potential energy, caused by the difference in the amount of electric potential energy one coulomb of charge feels between the two points A and B. (if the battery has an electric potential difference of 12V, the electron will deliver 12 joules of energy when going around the electric circuit from A to B)

So the electric field determines what the electric force would be on a test charge in that field.
The electric potential determines what the electric potential energy will be on a test charge.

My question: Does the electric potential determine what the electric potential energy would be on a test charge IN AN ELECTRIC FIELD? Because, what is then the difference between the electric force on a test charge and the electric potential energy on the test charge OTHER THAN THE UNITS Joules and Netwons?

 

[sophiecentaur]

My question: Does the electric potential determine what the electric potential energy would be on a test charge IN AN ELECTRIC FIELD? Because, what is then the difference between the electric force on a test charge and the electric potential energy on the test charge OTHER THAN THE UNITS Joules and Netwons?

I don't understand your question and I don't see why you want to extend on the correct definitions of potential in terms of joules per coulomb or the integral of work done in an electric field. (I think you may be ignoring the 'Integral' in the question above.) It is definitely not 'just units'.

The integral of the work done is really the more fundamental and, if you really wanted to, you could do all your calculations for electric circuits that way - step by step through all components and wires. But why would you want to? It would just be like making love standing up in a hammock - a lot of hard work to produce the same result.

There are many instances in Science where two different approaches can achieve the same end (just take waves and photons as an example) but there is usually one particular way which gives the result in any situation with less hassle.

 

[KitchiRUs]

My question: Does the electric potential determine what the electric potential energy would be on a test charge IN AN ELECTRIC FIELD? Because, what is then the difference between the electric force on a test charge and the electric potential energy on the test charge OTHER THAN THE UNITS Joules and Netwons?

Well, you could think of it this way - The electric force is the thing that pushes and pulls the test charge around. Like if you yank a ball on a string, the force of the string pulling the ball is what is moving the ball. The electric potential energy on the other hand, is the energy *possessed by* the test charge. Think of a situation where you are dropping the ball while standing on a ladder. It'll hit the ground faster than if you're on the ground and dropping it. The ball from the first case has a higher potential energy.

Although you should realize that there's a difference when it comes to electric potential energy - You've already said it. It's the energy required to bring the test charge to the point in the electric field from a point in infinity (so far away that the field is zero).

 

[sophiecentaur]

Well, you could think of it this way - The electric force is the thing that pushes and pulls the test charge around. Like if you yank a ball on a string, the force of the string pulling the ball is what is moving the ball. The electric potential energy on the other hand, is the energy *possessed by* the test charge. Think of a situation where you are dropping the ball while standing on a ladder. It'll hit the ground faster than if you're on the ground and dropping it. The ball from the first case has a higher potential energy.

Although you should realize that there's a difference when it comes to electric potential energy - You've already said it. It's the energy required to bring the test charge to the point in the electric field from a point in infinity (so far away that the field is zero).

Is this not just adding complication? If you are considering the ball 'hitting the ground' then you will need to specify where the ground is. Electric Potential, as you say, is defined referred to infinity and Potential Difference is defined as the difference for two locations. When you say "it will hit the ground faster", I assume you mean it's Kinetic Energy is greater and you aren't referring to how long it will take.
As far as I can see, the only problem in this thread is that there seems to be a bit of confusion between force and work, in that there is an implication that they are the same.

 

[KitchiRUs]

Well, yes, you have a point. I was just trying to get the picture across of the 'potential to do work' as potential energy. It's not always accurate, but it helped me figure out how to start thinking about it.

To attempt a more precise answer to christian0710's question -
Yes, the electric potential at a point in the field is the potential energy that would be possessed by a test charge at that point.
But as sophie has pointed out, force and energy are not the same thing. The energy of a body/particle/test charge can be changed by a force acting on it. This is a crude way of explaining it, but it'll help to start figuring out the difference.